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Criteria of univalence for a certain integral operator

100%

Ignaciuk S. , Parol M.

2019

tom 73

nr 1

In this article we consider the problem of univalence of a function introduced by Breaz and Ularu, improve some of their results and receive not only univalence conditions but also close-to-convex conditions for this function. To this aim, we used our method based on Kaplan classes.

Generalized sampling operators in modular spaces

88%

Mantellini I.

tom [Z] 38

77-92

On some shift invariant integral operators, univariate case

63%

Anastassiou G. , Gonska H.

nr 3

225-243

In recent papers the authors studied global smoothness preservation by certain univariate and multivariate linear operators over compact domains. Here the domain is ℝ. A very general positive linear integral type operator is introduced through a convolution-like iteration of another general positive linear operator with a scaling type function. For it sufficient conditions are given for shift invariance, preservation of global smoothness, convergence to the unit with rates, shape preserving and preservation of continuous probabilistic functions. Finally, four examples of very general specialized operators are presented fulfilling all the above properties; in particular, the inequalities for global smoothness preservation are proven to be sharp.